Phase plane analysis for nonlinear and linear systems near (6,2)

In summary, the conversation is about asking for help with a Maple Lab problem involving finding the cure and trajectories in a red rectangular region. The user provides code and images of their progress so far, including plots of the phase plane for a nonlinear and linear system near (2,-2) and (0,0). They then mention modifying the commands to produce plots near (6,2) and state that they have figured it out.
  • #1
tqh
2
0
i need help on this part, does anyone have any idead about maple lab? I should get the cure and trajectories in the red rectangular. But i try to fix the points and range, i still didn't get it

http://img193.imageshack.us/img193/387/deqp.jpg

Code:
trange1 := -3..3: window1 := x=1..3,y=-3..-1: 
inits1:=[[x(0)=2.5,y(0)=-1.5],[x(0)=1.5,y(0)=-1.5],[x(0)=1.5,y(0)=-2.5],
   [x(0)=2.5,y(0)=-2.5],[x(0)=2+2.0/3.0,y(0)=-2+(3.0-sqrt(17.0))/3.0]]:
DEplot([dex,dey],[x(t),y(t)],t=trange1,inits1, window1,color=GREEN,
   linecolor=[RED,BLUE,CYAN,PLUM,BLACK],thickness=2,stepsize=0.002,
   title="Phase plane near (2,-2): nonlinear system");

F1:=4*u+0*v; 
G1:=6*u+6*v;
dex1:=diff(x(t),t)=eval(F1,{u=x(t),v=y(t)});
dey1:=diff(y(t),t)=eval(G1,{u=x(t),v=y(t)});
DEplot([dex1,dey1],[x(t),y(t)],t=trange2,inits2, window1,color=GREEN,linecolor=[RED,BLUE,CYAN,PLUM,YELLOW],thickness=2,stepsize=0.002,
title="Phase plane near (0,0): linearized system");

Modify the above commands to produce plots of the phase plane for the nonlinear and linear systems near (6, 2). There are no straight line trajectories to consider in this case..

 
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  • #2
ohh i figured this out... thank you for visiting
 

Related to Phase plane analysis for nonlinear and linear systems near (6,2)

1. What is a nonlinear system in Maple?

A nonlinear system in Maple is a set of equations that cannot be solved using traditional linear methods. Instead, nonlinear systems require more advanced techniques such as numerical methods or approximation algorithms.

2. How do I solve a nonlinear system in Maple?

To solve a nonlinear system in Maple, you can use the solve command or the fsolve command. The solve command is used to find exact solutions, while the fsolve command uses numerical methods to approximate solutions.

3. Can Maple graph solutions to a nonlinear system?

Yes, Maple has built-in graphing capabilities that allow you to visualize the solutions to a nonlinear system. You can use the plot command to graph the solutions or use the interactive plot builder to customize your graph.

4. Are there any limitations to solving nonlinear systems in Maple?

While Maple has powerful capabilities for solving nonlinear systems, there are some limitations. For example, Maple may not be able to find exact solutions for very complex systems. In these cases, it may be necessary to use other software or approximation methods.

5. Can Maple handle systems with multiple variables?

Yes, Maple is able to handle systems with multiple variables. However, as the number of variables increases, the solving process may become more complex and time-consuming. It is important to carefully consider the complexity of your system before attempting to solve it in Maple.

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